# How do you differentiate #x^2arcsinx#?

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To differentiate (x^2\arcsin(x)), use the product rule:

[ \frac{d}{dx} \left( x^2\arcsin(x) \right) = x^2 \frac{d}{dx} \left( \arcsin(x) \right) + \arcsin(x) \frac{d}{dx} \left( x^2 \right) ]

Apply the chain rule to (\arcsin(x)) and the power rule to (x^2):

[ \frac{d}{dx} \left( x^2\arcsin(x) \right) = x^2 \cdot \frac{1}{\sqrt{1-x^2}} + 2x \arcsin(x) ]

So, the derivative of (x^2\arcsin(x)) is (x^2 \cdot \frac{1}{\sqrt{1-x^2}} + 2x \arcsin(x)).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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